Question

mark the correct theorem
aas asa sss sas hl
save and exit
(image of triangle with points f, g, j, h)

Explanation:

Step1: Analyze triangle markings

From the diagram, we see that two sides of the triangles (around the vertical line) are marked as equal (the tick marks), and the vertical angles at \( G \) are equal. Also, the horizontal lines ( \( F - \) and \( J - H \)) are marked as parallel or equal? Wait, actually, looking at the triangle congruence: the sides \( FG \) and \( JG \) (tick marks), \( HG \) and \(... \) Wait, the key is SSS: if three sides are equal. Wait, the diagram shows that \( FG = JG \) (tick), \( HG =... \) Wait, maybe the triangles \( FGH \) and \( JGH \)? Wait, no, the intersection at \( G \). Wait, the SSS (Side - Side - Side) criterion: if three sides of one triangle are equal to three sides of another triangle, they are congruent. The markings here (the tick marks on two sides and the vertical line which is a common side? Wait, maybe the triangles \( F G... \) and \( J G... \) have three sides equal. So SSS is a valid criterion here. Also, SAS: but SSS is more likely if all three sides are marked. Wait, the options: AAS, ASA, SSS, SAS, HL. The diagram has tick marks on two sides (so two sides equal) and the vertical angles (which are equal, but also the third side? Wait, maybe the horizontal sides are equal (the arrows, indicating parallel or equal length). So if \( FG = JG \), \( HG =... \) no, maybe the three sides: \( FG = JG \), \( HG =... \) Wait, the SSS option is marked, so likely SSS is correct. Also, the other options: ASA (angle - side - angle), SAS (side - angle - side), AAS (angle - angle - side), HL (hypotenuse - leg for right triangles). Since the diagram has side markings (tick marks) on two sides and the third side (the horizontal one) is equal (arrows), so SSS is appropriate.

Step2: Confirm the congruence criterion

The SSS (Side - Side - Side) congruence criterion states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. From the diagram, the tick marks on two sides and the equal horizontal sides (implied by the arrows) suggest that all three sides are equal, so SSS is the correct criterion. Also, the other options: ASA requires two angles and the included side, SAS requires two sides and the included angle, AAS two angles and a non - included side, HL is for right triangles. Since there's no right angle indicated and the markings are on sides, SSS is the best fit.

Answer:

SSS (the option labeled "SSS")